1. Field of the Invention
The present invention relates to a self-compensating spiral spring for a mechanical balance-spiral spring oscillator for a watch or clock movement or other precision instrument, made of an Nbxe2x80x94Hf paramagnetic alloy possessing a positive thermal coefficient of Young""s modulus (TCE), capable of compensating for the thermal expansion of both the spiral spring and the balance.
2. Description of the Related Art
All the methods proposed for compensating for these frequency variations are based on the consideration that this natural frequency depends exclusively on the ratio of the constant of the restoring torque exerted by the spiral spring on the balance to the moment of inertia of the latter, as indicated in the following equation:                     F        =                              1                          2              ⁢              π                                ⁢                                    C              I                                                          (        1        )            
where
F=natural frequency of the oscillator;
C=constant of the restoring torque exerted by the oscillator""s spiral spring;
I=moment of inertia of the oscillator""s balance.
Since the discovery of alloys based on Fexe2x80x94Ni possessing a positive thermal coefficient of Young""s modulus (hereafter called TCE), the thermal compensation of the mechanical oscillator is obtained by adjusting the TCE of the spiral spring according to the thermal expansion coefficients of the spiral spring and of the balance. This is because, by expressing the torque and the inertia on the basis of the characteristics of the spiral spring and the balance, and then differentiating equation (1) with respect to temperature, the relative thermal variation in the natural frequency is obtained, namely:                                           1            F                    ⁢                                    ⅆ              F                                      ⅆ              T                                      =                              1            2                    ⁢                      (                                                            1                  E                                ⁢                                                      ⅆ                    E                                                        ⅆ                    T                                                              +                              3                ⁢                                  α                  s                                            -                              2                ⁢                                  α                  b                                                      )                                              (        2        )            
where:
E: Young""s modulus of the spiral spring of the oscillator;             1      E        ⁢                  ⅆ        E                    ⅆ        T              =            T      ⁢              xe2x80x83            ⁢      C      ⁢              xe2x80x83            ⁢      E        =                                                      thermal              ⁢                              xe2x80x83                            ⁢              coefficient              ⁢                              xe2x80x83                            ⁢              of              ⁢                              xe2x80x83                            ⁢                              Young                '                            ⁢              s                        ⁢                          xe2x80x83                                                                                      xe2x80x83                        ⁢                          modulus              ⁢                              xe2x80x83                            ⁢              of              ⁢                              xe2x80x83                            ⁢              the              ⁢                              xe2x80x83                            ⁢              spiral              ⁢                              xe2x80x83                            ⁢              spring                        ⁢                          xe2x80x83                                                                                      xe2x80x83                        ⁢                                          of                ⁢                                  xe2x80x83                                ⁢                the                ⁢                                  xe2x80x83                                ⁢                oscillator                            ;                                          
xcex1s: thermal expansion coefficient of the spiral spring of the oscillator;
xcex1b: thermal expansion coefficient of the balance the oscillator.
By adjusting the self-compensation term   A  =            1      2        ⁢          (                        T          ⁢                      xe2x80x83                    ⁢          C          ⁢                      xe2x80x83                    ⁢          E                +                  3          ⁢                      α            s                              )      
to the value of the thermal expansion coefficient of the balance, it is possible to make equation (2) equal to zero. Thus, the thermal variation in the natural frequency of the mechanical oscillator can be eliminated.
The thermal expansion coefficient xcex1b of the materials for balances most often used, such as alloys of copper, of silver, of gold, of platinum or of steel, lie within a range of about 10 to 20 ppm/xc2x0 C. To compensate for the effects of the temperature variations on the natural frequency of the oscillators due to their expansion, the alloys for spiral springs must therefore have a corresponding self-compensation term. The desired accuracy of watches means that the self-compensation term must be able to be controllably adjusted in manufacture with a tolerance of a few ppm/xc2x0 C. about the desired value.
The ferromagnetic alloys based on iron, nickel or cobalt currently used for manufacturing spiral springs possess an abnormally positive TCE within an approximately 30xc2x0 C. range around room temperature, due to the proximity of their Curie temperature. Near this temperature, the magnetostrictive effects which decrease the Young""s modulus of these alloys disappear, resulting in an increase in the modulus. Apart from the fact that this temperature range is relatively narrow, these alloys are sensitive to the effects of magnetic fields. The latter modify the elastic properties of spiral springs in an irreversible manner and consequently change the natural frequency of the mechanical oscillator. Furthermore, the elastic properties of ferromagnetic alloys vary with the degree of cold working, which means that this parameter has to be precisely controlled during manufacture of the spiral spring.
The desired TCE values of spiral springs produced from this family of alloys are adjusted by a precipitation heat treatment which also fixes the final shape of the spiral spring by relaxation.
As an alternative to ferromagnetic alloys for the manufacture of precision springs and self-compensating spiral springs, paramagnetic alloys having a high magnetic susceptibility and a negative thermal coefficient of susceptibility have already been proposed in CH-551 032 (D1) , in CH-557 557 (D2) and in DE-C3-15 58 816 (D3). These alloys possess an abnormally positive TCE and have the advantage of having elastic properties which are insensitive to magnetic fields. Their elastic properties depend on the texture created during the drawing of the spiral spring, but little on the deformation ratio, unlike ferromagnetic alloys. In addition, as mentioned in document D3, these alloys offer a thermal compensation range for mechanical oscillators which extends over more than 100xc2x0 C. about room temperature.
The physical causes which create the abnormally positive TCE of these paramagnetic alloys are explained in the abovementioned documents. According to the latter, these alloys possess a high density of electron states at the Fermi level and strong electron-phonon coupling, thereby producing this abnormal behavior of the TCE.
In particular, document D3 cites, as being suitable for the manufacture of oscillator spiral springs of watch or clock movements, alloys in which Nb or Ta is alloyed with Zr, with Ti or with Hf which are found in these alloys in proportions such that they are capable of precipitating in two phases.
Furthermore, EP 0 886 195 (D4) proposes an Nbxe2x80x94Zr alloy containing between 5% and 25% by weight of Zr and at least 500 ppm by weight of a doping agent at least partly formed from oxygen. With this alloy, the TCE is controlled by the texture. The participation which occurs during the fixing process induces recrystallization which modifies the texture and allows the TCE to be adjusted. Oxygen has an influence on the precipitation and the crystallization, and therefore on the TCE.
Adjustment of the TCE during the fixing operation is difficult to control. This is because the texture which controls the TCE is modified by the recrystallization during the fixing operation. Now, in Nbxe2x80x94Zrxe2x80x94O alloys, the initiation of recrystallization and its development depend on the oxygen concentration, on the deformation ratio and on temperature. With these alloys, it has been found that the temperature range over which recrystallization develops is very narrow (approximately 50xc2x0 C.). In addition, the induced variation in TCE between the start and end of recrystallization is large, about 150 ppmxc2x0 C. The narrow temperature range within which recrystallization develops and this large variation in TCE mean that it is difficult to make the TCE adjustment of Nbxe2x80x94Zrxe2x80x94O alloys reproducible. The narrowness of this temperature range is due to the fact that this reaction is initiated by the participation of Zr-rich phases from the solid solution.
Although document D3 is based on the ability of the components of the alloy to precipitate in two phases, the spring with an abnormally positive TCE is manufactured from the alloy annealed at high temperature and then rapidly cooled so as to obtain a supersaturated solid solution. In this state, the alloy then undergoes cold deformation with a deformation ratio of more than 85%. This high degree of deformation induces a texture favorable to a positive TCE. To adjust the TCE to the desired value, the alloy is finally heat treated within a temperature interval which allows precipitation from the supersaturated solid solution. The phases which precipitate from the solid solution have lower TCEs, which results in a decrease in the overall TCE and allows it to be adjusted to the desired value. The recrystallization after two-phase precipitation is relatively difficult to control. Furthermore, in the case of Hf, the proportion of Hf must be greater than 30 at %, since up to this concentration this element is in solid solution in the Nb. Hence the deformability is thereby reduced.
The object of the present invention is to obtain an alloy which makes it possible to remedy, at least partly, the drawbacks of the abovementioned alloys.
Surprisingly, it has been discovered that Nbxe2x80x94Hf alloys having very low proportions of Hf, that is to say proportions which lie well below the limit above which Hf precipitates, allow a positive TCE to be obtained, this limit being lowered down to 2 at %.
The subject of the invention is consequently a self-compensating spiral spring for a mechanical balance-spiral spring oscillator for a watch or clock movement or other precision instrument, made of an Nbxe2x80x94Hf paramagnetic alloy possessing a positive thermal coefficient of Young""s modulus (TCE), which is able to compensate for the thermal expansion both of the spiral spring and the balance.